air base; for road railroad, and pipeline alignment; forthe control of hydrographic surveys; and for many otherprojects. A traverse is always classified as either a closedtraverse or an open traverse. A closed traverse starts andends at the same point or at points whose relativehorizontal positions are known. An open traverse endsat the station whose relative position is not previouslyknown and, unlike a closed traverse, provides no checkagainst mistakes and large errors. In the EA3TRAMAN, you studied field procedures for laying outtraverses. In this chapter you will study computationsthat are necessary for adjusting and determining theareas of traverses.Checking and Reducing AnglesBegin traverse computations by checking to makesure that all the required angles (including closingangles) were turned and that the notes correctly indicatetheir sizes. For deflection angles, check to make surethat angles marked L or R were actually turned and havebeen turned in those directions. Check your sketches andbe sure they agree with your field notes. Next, youreduce repeated angles to mean angles using theprocedures that you learned in the EA3 TRAMAN.Checking and Reducing DistancesCheck to make sure that all required linear distanceshave been chained. Reduce slope distances whenneeded. If you broke chain on the slopes, you check tomake sure that the sums of break distances werecorrectly added.Finally, you should apply standard error, tension,and temperature corrections if needed.Adjusting AnglesFrom your study of the EA3 TRAMAN, you shouldrecall the following three conditions for a closedtraverse: (1) the theoretical or geometrical sum of theinterior angles is 180° x (n – 2), n being the number ofangles measured; (2) the sum of the exterior angles is180° x (n + 2), where n = number of angles measured;and (3) the difference between the sum of the rightdeflection angles and the sum of the left deflectionangles is 360°. Any discrepancy between one of thesesums and the actual sum of the angles as turned ormeasured constitutes the angular error of closure.You adjust the angles in a closed traverse bydistributing an angular error of closure that is within theallowable maximum equally among the angles.Figure 7-7.—Closed traverse by deflection-angle method.Figure 7-7 shows a traverse in which one of thedeflection angles was turned to the lefft, all others to theright. The sum of the right deflection angles is 444°59'.Then, by subtracting the left deflection angle (85°01'),you find that the angular error of closure is 02', whichis an average of 20" per deflection angle. This averageangular error of closure is then added to each rightdeflection angle and subtracted from each leftdeflection angle. After applying this adjustment to eachdeflection angle in this example, you find, then, that thesum of the adjusted angles to the right equals 445°00'40"and that the sum of the left angles (of which there is onlyone) is 85°00'40". The difference between these valuesis 360°00'00", as it should be.Remember that in adjusting the angles in adeflection-angle traverse, you apply the adjustments toright and left angles in opposite direction.Adjusting for Linear Error of ClosureThe procedure for distributing a linear error ofclosure (one within the allowable maximum, of course)over the directions and distances in a closed traverse iscalled balancing or closing the traverse. Before you canunderstand how to do this, you must have a knowledgeof latitude and departure.LATITUDE AND DEPARTURE.— Latitude anddeparture are values that are employed in the methodof locating a point horizontally by its plane coordinates.In the plane coordinate system, a point of origin isarbitrarily y selected for convenience. The location of apoint is given in terms of its distance north or south andits distance east or west of the point of origin. The planecoordinate system will be explained later in this chapter.7-8
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